Strange twisting from multi-chain armature
The problem is 3 chains per hair strand combined with that you skipped many segments an created long bones over them, so the bones cannot follow the mesh strand exactly. They try their best to fit the shape, but this results in twisting at the tip:



The 2 side chains are redundant. Build only 1 chain but for every segment and set the bones like this so they rotate with the mesh:



You cannot notice any folding in the strands anyway, you will hardly see any difference.

If you really want to copy the motion exactly, rather than setting up 3 chains for each strand segmented like crazy write a script that will generate disconnected bones on every face and constrain each to that particular face with a Child Of with vertex group of that face. Child Of Constraint Set Inverse with Python

Also this simulation is not very high quality, the mesh oscillates with high frequency and you can see some nasty artifacts (but that does not cause the problem)

In the armature modifier check Preserve Volume (that does Quaternion skinning which you want)